First, let's get what the definition of a yandere is out of the way, or to at least clarify. To preface, this is both my personal definition or the one that I've come to better understand, as well as the contrasting differences between the more popularized "media" variant of it.
The definition, as defined by the Japanese translation and more frequently used in media, is as follows:
The difference, however, is that the media portrays the yandere often times as being more “snappy” with their actions. Often splitting from a heartwarming personality to more violent behaviours, in the case of shows/anime, these actions being murder, violence, mania and the other shticks associated with them. This is the influence and reflection of how Yandere is used for their shock value in popularized media. A prime example of these traits exhibited in a character would be Yuno Gasai from Mirai Nikki, who has become one of the most popular yanderes out there.
However, I find that the definition that the media has created, the aforementioned mania, violence and murder, is folly as a reflection of the real-life and fictional applications of the term. Yandere isn’t characterized by the murder, all the violence, the snappy behaviour and the desire to kill. Yandere is someone who is obsessive over an individual, which leads to multiple obsessive behaviours, spanning from possessiveness, overprotectiveness, the want for co-dependency and/or otherwise. Taking it back to the literal definition, it’s being head over heels for them, to the degree of being in love, but cases can vary and can range from friends to significant others (or romantic interests). As said, the term isn’t those who are maniacal, like how the media portrays it and additionally so for shock value. Watching Mirai Nikki and expecting everyone who can relate to the term yandere, should not mean that’s how all of them act, nor should it be an intrinsic definition to base someone on. It’s not applicable to say that a fictional yandere character, or a yandere in general, is how all of them should and would act.
The problem with the media’s portrayal of yandere is how fixated they are on the shock value, forgetting to go into how or why yanderes feel the things they do. When it comes to determining who is and who isn’t yandere, it’s important to look into the intention, as it is what defines them the most. If someone is prone to snap, with or without a partner, as well as being seemingly violent and has no true intent in wanting to always protect the ones they love, they are more apt to be called a yangire. Real life people can and won’t always do these sorts of things, and it’s not feasible to say that they would since it’d be like saying anyone who kills with the slight intention to protect another is yandere, which is obviously not the case. As such, if their primary concern is the person they’re obsessing over, as well as doing it for them, that’s what makes them yandere.
This isn’t to say that they can’t be enjoyable to watch, that’s not what I’m getting at, it’s that they don’t always portray the proper image of how a yandere would actually think in regards to their love. They’re characterised by their intent, their obsessive qualities, and especially their love for the aforementioned person. It’s how they feel protective over them while doing things that are for them, not out of disregard for them or doing it for the sake of killing, that matter.
That’s my take on it, anyway, thanks for reading!